The temperaments listed are 27edo-distinct, meaning that they are all different even if tuned in 27edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 27e val (<27 43 63 76 94 100|) was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period, generator	Wedgie	Name	Complexity	Commas
27, 11	<<1 9 12]]	Superpyth	2.947	20480/19683
27, 8	<<2 -9 -19]]	Beatles	3.798	524288/492075
9, 2	<<3 0 -7]]	Augmented	1.549	128/125
27, 4	<<4 9 5]]	Tetracot	2.783	20000/19683
27, 13	<<5 -9 -26]]	Fervor	4.996	67108864/61509375
9, 1	<<21 -27 -92]]		17.661	|92 -27 -21>
27, 10	<<7 9 -2]]	Sensi	3.407	78732/78125
27, 2	<<8 -9 -33]]		6.348	8589934592/7688671875
3, 1	<<9 -27 -64]]		12.515	|64 -27 -9>
27, 7	<<10 9 -9]]	Myna	4.502	10077696/9765625
27, 1	<<11 18 3]]	Quartonic	6.026	390625000/387420489
9, 4	<<12 -27 -71]]		13.72	|71 -27 -12>
27, 5	<<13 9 -16]]	Kumonga	5.808	1289945088/1220703125

7-limit temperaments

Period, generator	Wedgie	Name	Complexity	Commas
27, 11	<<1 9 -2 12 -6 -30]]	Superpyth	2.874	64/63 245/243
27, 8	<<2 -9 -4 -19 -12 16]]	Beatles	3.125	64/63 686/675
9, 2	<<3 0 -6 -7 -18 -14]]	Augene	2.336	64/63 126/125
27, 4	<<4 9 19 5 19 19]]	Wollemia	3.995	126/125 2240/2187
27, 13	<<5 -9 -10 -26 -30 2]]	Fervor	4.710	64/63 9604/9375
9, 1	<<6 0 15 -14 7 35]]	Semiaug	3.844	128/125 245/243
27, 10	<<7 9 13 -2 1 5]]	Sensi	3.080	126/125 245/243
27, 2	<<8 18 11 10 -5 -25]]	Octacot	4.551	245/243 2401/2400
3, 1	<<9 0 9 -21 -11 21]]	Niner	3.907	128/125 686/675
27, 7	<<10 9 7 -9 -17 -9]]	Myna	3.731	126/125 1728/1715
27, 1	<<11 18 5 3 -23 -39]]	Quartonic	5.395	1728/1715 4000/3969
9, 4	<<12 0 3 -28 -29 7]]	Oodako	5.164	128/125 2401/2400
27, 5	<<13 9 1 -16 -35 -23]]	Kumonga	5.411	126/125 12288/12005

11-limit temperaments

Period, generator	Wedgie	Name	Complexity	Commas
27, 11	<<1 9 -2 16 12 -6 22 -30 6 52]]	Superpyth	3.410	64/63 100/99 245/243
27, 8	<<2 -9 -4 5 -19 -12 1 16 43 28]]	Ringo	3.126	56/55 64/63 540/539
9, 2	<<3 0 -6 -6 -7 -18 -20 -14 -14 4]]	Augene	2.286	56/55 64/63 100/99
27, 4	<<4 9 19 10 5 19 2 19 -8 -38]]	Wollemia	3.472	56/55 100/99 243/242
27, 13	<<5 -9 -10 -1 -26 -30 -19 2 29 32]]	Fervor	4.112	56/55 64/63 1350/1331
9, 1	<<6 0 15 15 -14 7 3 35 35 -10]]	Hemiaug	3.575	56/55 128/125 245/243
27, 10	<<7 9 13 4 -2 1 -18 5 -22 -34]]	Sensis	2.980	56/55 100/99 245/243
27, 2	<<8 18 11 20 10 -5 4 -25 -16 18]]	Octacot	4.070	100/99 243/242 245/242
3, 1	<<9 0 9 9 -21 -11 -17 21 21 -6]]	Niner	3.394	56/55 128/125 540/539
27, 7	<<10 9 7 -2 -9 -17 -38 -9 -36 -30]]	Coleto	4.019	56/55 100/99 1728/1715
27, 1	<<11 18 5 14 3 -23 -16 -39 -30 22]]	Quarto	4.675	100/99 245/242 864/847
9, 4	<<12 0 3 3 -28 -29 -37 7 7 -2]]	Oodako	4.551	56/55 128/125 3773/3750
27, 5	<<13 9 1 19 -16 -35 -15 -23 13 50]]	Kumonga	4.924	126/125 176/175 864/847

13-limit temperaments

Period, generator	Wedgie	Name	Complexity	Commas
27, 11	<<1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14]]	Superpyth	3.228	64/63 78/77 91/90 100/99
27, 8	<<2 -9 -4 5 -1 -19 -12 1 -9 16 43 31 28 12 -22]]	Ringo	2.798	56/55 64/63 78/77 91/90
9, 2	<<3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64]]	Ogene	2.936	56/55 64/63 91/90 100/99
27, 4	<<4 9 -8 10 -2 5 -24 2 -18 -44 -8 -38 56 24 -44]]	Modus	3.607	64/63 78/77 100/99 144/143
27, 13	<<5 -9 -10 -1 -16 -26 -30 -19 -44 2 29 -4 32 -8 -52]]	Fervor	4.175	56/55 64/63 78/77 507/500
9, 1	<<6 0 15 15 -3 -14 7 3 -27 35 35 -7 -10 -64 -66]]	Hemiaug	3.785	56/55 91/90 128/125 245/243
27, 10	<<7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20]]	Sensis	2.664	56/55 78/77 91/90 100/99
27, 2	<<8 18 11 20 23 10 -5 4 7 -25 -16 -13 18 24 6]]	Octocat	3.773	78/77 91/90 100/99 245/242
3, 1	<<9 0 9 9 9 -21 -11 -17 -19 21 21 21 -6 -8 -2]]	Niner	3.035	56/55 78/77 91/90 128/125
27, 7	<<10 9 7 25 22 -9 -17 5 -2 -9 27 18 46 36 -16]]	Minah	3.862	78/77 91/90 126/125 176/175
27, 1	<<11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24]]	Quarto	4.328	78/77 100/99 144/143 245/242
9, 3	<<12 0 3 3 -6 -28 -29 -37 -54 7 7 -14 -2 -28 -32]]	Oodako	4.551	56/55 78/77 128/125 507/500
27, 5	<<13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46]]	Kumonga	4.509	78/77 126/125 144/143 176/175